To better answer your question, how wide on average is the Little Red River? And on second thought, that's not the definitive question. Since you've been fly fishing a while, you have some idea of your preferred style, which roughly fits one of these two categories:

1) Fishing the water; meaning that you're casting to work your fly through suitable holding water at whatever practical distance. Here the size of the stream matters, and tackle gets chosen to cover the normal casting distances. On big rivers, trout tackle can be indistinguishable from what steelhead or salmon anglers use.

2) Fishing over visable fish; meaning that they're either rising to the surface, or they're lying in sight, usually in shallow water. Here presentation counts, not distance; you're typically making accurate casts at twenty-forty feet, regardless of the size of the stream.